Advanced dropdown stops applying the Search Filter while the search text remains after clicking the header back Button during a Search

Steps to reproduce:

1. Create any project and select a GameObject in a Scene
2. In the Inspector, click "Add Component"
3. Enter a category that has sub-items (e.g. "Physics") so the header "<" back button appears
4. Type a query into the search field (e.g. "rigid")
5. While the search text is still present, click the header "<" back button (top-left)

Actual results: The search field keeps the typed text, but the list shows the full
unfiltered contents of the level and the search is no longer applied. Navigating into
sub-categories continues to show everything unfiltered. Deleting the search text snaps
back to the level where the search started

Expected results: The dropdown does not end up in a state where the search field shows a query but the list ignores it. Pressing the header "<" during a search should behave like the keyboard Left-arrow already does (which stays in the search field and does not navigate), or it should clear the search so the list matches the empty field

Reproducible with versions: 6000.0.77f1, 6000.3.16f1, 6000.4.12f1, 6000.5.0f1, 6000.6.0a7

Tested on (OS): Windows 11

Notes:

• Reproduces in all advanced dropdowns built on the same control
• Only the mouse header "<" button triggers it; the keyboard Left-arrow during a search correctly stays in the search field and does not navigate. The keyboard back path is intentionally suppressed during search, but the header "<" button is not - so the two paths disagree and the header path leaves the dropdown in an inconsistent state.